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Nonlinear dynamic analysis for coupled vehicle-bridge system with harmonic excitation

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Abstract

In this paper, a multi-degree-of-freedom lumped parameter coupled vehicle-bridge dynamic model is proposed considering the nonlinearities of suspension and tire stiffness/damping and the nonlinear foundation of bridge. In terms of modelling, the continuous expressions of the kinetic energy, potential energy and the dissipation function are constructed. The dynamic equations of the coupled vehicle-bridge system (CVBS) are derived and discretized using Galerkin’s scheme, which yield a set of second-order nonlinear ordinary differential equations with coupled terms. The numerical simulations are conducted by using the Newmark-β integration method to perform a parametric study of the effects on excitation amplitude, suspension stiffness and position relation. The bifurcation diagram, 3-D frequency spectrum and largest Lyapunov exponent are demonstrated in order to better understand the vibration properties and interaction between the vehicle and bridge with the key system parameters. It can be found that the nonlinear dynamic characteristics such as parametric resonance, jump phenomena, periodic, quasi-periodic and chaotic motions are strongly attributed to the interaction between vehicle and bridge. Significantly, under the combined internal and external excitations, the vibration amplitudes of the CVBS have a certain degree of dependence on the external excitation. Suspension stiffness could lead to complex dynamics such as the higher-order bifurcations increase and the chaotic regions broaden. The increasing of distance could effectively control the nonlinear vibration of CVBS. The application of the proposed nonlinear coupled vehicle-bridge model would bring higher computational accuracy and make it possible to design the vehicle and bridge simultaneously.

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Acknowledgements

This study was funded by collaborative Innovation Center of Major Machine Manufacturing in Liaoning, National Support Program, the key common technology research and demonstration of paving equipment for subgrade in alpine (No. 2015BAF07B07) and the authors gratefully acknowledge the financial support provided by Natural Science Foundation of China (No. 51475084).

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Authors and Affiliations

  1. School of Mechanical Engineering and Automation, Northeastern University, Shenyang, 110819, China

    Shihua Zhou, Guiqiu Song, Zhaohui Ren & Bangchun Wen

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  1. Shihua Zhou
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  2. Guiqiu Song
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  3. Zhaohui Ren
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  4. Bangchun Wen
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Correspondence to Guiqiu Song.

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Zhou, S., Song, G., Ren, Z. et al. Nonlinear dynamic analysis for coupled vehicle-bridge system with harmonic excitation. Meccanica 52, 2219–2243 (2017). https://doi.org/10.1007/s11012-016-0577-x

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  • DOI: https://doi.org/10.1007/s11012-016-0577-x

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